Flow cytometry data processing for antimicrobial agent sensibility prediction

ABSTRACT

where Mode(ATB) and QT(ATB) are the first and second coordinate values with the antimicrobial agent concentration, and Mode(no ATB) and QT(no ATB) are respectively the first and second coordinate values without the antimicrobial agent concentration.

FIELD OF THE INVENTION

The invention relates to the prediction of sensibility of amicroorganism to an antimicrobial agent using flow cytometry, inparticular sensibility of a bacteria to an antibiotic.

BACKGROUND OF THE INVENTION

As known per se, two critical concentrations, or “breakpoints”, aredefined for a antimicrobial agent, and if the minimal inhibitoryconcentration (“MIC”) measured for a microorganism is lower than thefirst breakpoint the microorganism is susceptible to said agent, if themeasured MIC is greater than the second breakpoint the microorganism isresistant to said agent, and if the measured MIC is in between themicroorganism is intermediate to said agent. The gold-standard methodscurrently used in laboratories to evaluate the MIC of a microorganism,and then its sensibility phenotype, to an antimicrobial agent areusually based on measurement of growth inhibition. These techniquesinclude the broth micro-dilution reference method as well as manual andautomated alternative methods such as Etest®, disk diffusion, agardilution, or VITEK 2® instrument, to name a few.

Over the past decades, studies have shown that early bacterialphysiological changes can be visualized by a wide array of commerciallyavailable fluorescent markers using flow cytometry (“FCM”) ormicroscopic/imaging-based technologies [1-5]. As it is well-known, flowcytometry basically consists in producing a liquid stream carryingaligned particles (e.g. microorganisms) which individually pass througha laser beam, and measuring an optical response to said beam of each ofthe particles, that is to say its fluorescence, its forward-scatteredlight and its side-scattered light. In particular FCM-based single-cellanalysis can allow fast monitoring of cell counts [6-10] or averagefluorescence intensities [11, 12] upon contact with antibiotics. Otherantibiotic-induced changes in cell morphology, size, light scatteringand auto-fluorescence properties can also be detected by FCM aspreviously reported in the literature [13-15]. In a recent patentapplication, the investigation of antibiotic susceptibility profilesthrough measurement of cell enlargement has been proposed but no robustanalysis method is described in order to define discriminatingthresholds between phenotypes [16]. So far, only weakly quantitative orarbitrary thresholds mostly based on ratios of distribution averageshave been used to differentiate susceptible from resistant populations.In addition, only few effort has been made to combine differentsignatures such as fluorescence and scattering data in order to addressthe complexity of the response to antimicrobials. Therefore, a robuststrategy that takes full advantage of FCM data information to buildrobust antibiotic susceptibility prediction algorithms is still lacking,despite numerous attempts to show the value of FCM for fast antibioticsusceptibility testing (“AST”).

For example, the patent application WO 2012/164547 A1 [17] describes amethod based on the use of breakpoint concentrations. Briefly, after afast incubation in the presence of antibiotic, bacteria are labeled witha fluorescent marker and analyzed by FCM. The ratios of meanfluorescence intensities (“MFI”) between antibiotic-treated anduntreated cells, also called staining indexes (“SI”), are calculated forboth susceptible and resistance reference breakpoint concentrations. Forinstance, if a fluorescence marker that labels live cells is used,susceptible strains are expected to exhibit low MFI values when treatedwith antibiotics. Therefore, the interpretation is as follows: a) ifSI<1 at the susceptible reference breakpoint, then a strain is predictedas being susceptible to the antibiotic; b) if SI>1 at the resistancereference breakpoint, then a strain is predicted as being resistant. Onthe opposite side, if a fluorescent marker that targets cell damage isused, susceptible strains are expected to exhibit high fluorescencevalues. Consequently, the interpretation is as follows: a) if SI>1 atthe susceptible reference breakpoint, then a strain is predicted asbeing susceptible strain; b) if SI<1 at the resistance referencebreakpoint, then a strain is predicted as being resistant.

Other studies have also used a similar approach [11]. The main drawbackof this method is that it is based solely on MFI values which are onlyaverage distributions that might underestimate or mask signalsoriginating from a small portion of an heterogeneous population. Inaddition, breakpoint concentrations are defined by reference methodbased on growth inhibition. However, they don't always correlate withearly changes that are detected by FCM. In this regard, other studieshave looked at the effect of antibiotics using subinhibitoryconcentrations [6], concentrations exceeding MIC values [18, 19] orconcentrations corresponding to susceptible breakpoints only [12].Therefore, by focusing only on breakpoint concentrations, importantinformation relative to other concentrations could be lost. Otherstudies have focused on two-dimensional analysis for betterdiscrimination of populations. Indeed, bi-parametric matricesrepresenting scattering vs. fluorescence [20, 21] or fluorescence 1 vs.fluorescence 2, in case of dual labeling [12], can emphasize subtledifferences between populations. Hence, discriminating cutoff values arecalculated from the number or percentage of cells that fall in specificregions of the 2D matrix upon contact with antibiotics. However, theseregions are often selected qualitatively thereby decreasing therobustness of the method. More recently, an initiative based on 3Danalysis of adaptively binned scattering and fluorescence signatures hasbeen published [1]. To date, this is the most advanced study showing anin-depth processing of FCM data to build a prediction algorithm for AST.As listed below, this method has several advantages over previousstrategies: a) in comparison to MFI values, the use of binned data canallow specific capture of subtle variations as discussed above; b) theadaptation of the binning strategy to the highest variance dimensionallows the selection of the most significant information from thepopulation; c) the 3D-multidimensional analysis combines forwardscatter, side scatter and fluorescence data for a more globalinvestigation of antibiotic-induced changes. However, this method mightfail to provide a robust analysis for several reasons:

-   -   in this study the authors define a discriminating threshold at        99% confidence using a susceptible strain treated with        antibiotics at 1/16×MIC concentrations. While the bar was set        quite low for susceptibility phenotype, their prediction model        does not include resistance phenotypes. Indeed, one resistance        strain was used only to validate a prediction model that was        build using a susceptible strain. Therefore, no discrimination        strategy that involves comparison between phenotypes is        proposed;    -   the authors do not describe the detection of intermediate        phenotypes;    -   for a potential application of their prediction model, the        authors propose the use of MIC concentrations of their        susceptible model strain. This method does not seem to be robust        as this antibiotic concentration was not sufficient to clearly        detect the susceptibility profile of another strain that        exhibited a higher MIC value (ex: Gentamicin). Therefore, this        document does not describe any development of a prediction model        using a specific concentration and the validation of the method        using a different concentration;    -   the prediction model proposed in this study is based on one        single susceptible strain. Due to the heterogeneity of response        to antibiotics depending on strains, phenotypes, MIC values, and        so on, the robustness of their method cannot be validated.

Despite numerous studies on FCM for fast antibiotic susceptibilitytesting (“AST”), there is still a need to predict, in a robust manner,the sensibility of microorganisms to a antimicrobial agent.

SUMMARY OF THE INVENTION

In particular, the MFI method fails to robustly quantify subtle effectof a antimicrobial agent. The invention aims at proposing propose arobust quantification of such effect.

To this end, a first object of the invention is a method for quantifyingthe sensibility of a test microorganism to a concentration of anantimicrobial agent comprising:

-   -   preparing at a two liquid samples comprising a population of the        test microorganism and a viability fluorescence marker targeting        the tested microorganism, one of said liquid sample comprising        the antimicrobial agent at said concentration and the another of        said liquid samples do not comprising the antimicrobial agent;    -   for each of said samples of the test microorganism, acquiring,        by means of a flow cytometer, a digital set of values comprising        a fluorescence distribution or a forward scatter distribution or        side scatter distribution of the population of microorganisms in        said sample;    -   for each of said samples, computing of:        -   a first coordinate value corresponding to the main mode of            the acquired distribution and an first area of the acquired            distribution for values greater than the first coordinate            value;        -   a second coordinate value, greater than said first            coordinate value, for which a second area of the acquired            distribution between said first and second coordinate values            equals a predefined percentage of the first area over 50%,    -   computing a ratio according to the relation:

$Q = \frac{{{QT}({ATB})} - {{Mode}({ATB})}}{{{QT}\left( {{no}\mspace{14mu} {ATB}} \right)} - {{Mode}\left( {{no}\mspace{14mu} {ATB}} \right)}}$

-   -   where Mode(ATB) and QT(ATB) are respectively the first and        second coordinate values with said concentration of        antimicrobial agent, and Mode(no ATB) and QT(no ATB) are        respectively the first and second coordinate values without said        concentration of antimicrobial agent.

In other words, the ratio Q is able to catch heterogeneous profiles ofthe acquired distribution, as one may observe on certain antimicrobialagent that effects only a part of the population of microorganismscontained in a liquid sample. In particular, the more the ratio Qdeviate from 1, the more the microorganism is sensible to theantimicrobial agent. According to the MFI method, the testedmicroorganism would be determined as resistant to the antimicrobialagent, while according to the invention said microorganism would bedetermined as being sensible.

The invention also aims at proposing a method and a system forpredicting the susceptibility, intermediate or resistant phenotype of amicroorganism to an antimicrobial agent by flow cytometry, which is fastand robust.

To this end, a second object of the invention is a method for predictingthe sensibility phenotype of a test microorganism to an antimicrobialagent amongst susceptible, intermediate and resistant phenotypes,comprising:

A. a learning stage comprising the following steps:

-   -   a. choose a set of microorganisms comprising susceptible,        intermediate an resistant phenotype microorganisms, said        phenotypes being determined based on a susceptible and a        resistant breakpoint concentrations of the antimicrobial agent,        and generate a digital set of sensibility phenotypes of said set        of microorganisms;    -   b. for each microorganism of the set of microorganisms, prepare        liquid samples comprising a population of said microorganism, a        viability fluorescence marker targeting said microorganism, and        the antimicrobial agent, said liquid samples comprising at least        two different concentrations of the antimicrobial agent;    -   c. for each sample, acquire, by means of a flow cytometer, a        digital set of values comprising a fluorescence distribution        and/or a forward scatter distribution and/or side scatter        distribution of the population of microorganisms in said sample;    -   d. for each microorganism of the set of microorganisms,        generate, by means of a computer unit, a feature vector based on        the sets of values acquired for said microorganism wherein        generation of the feature vector comprises, for each of the        different concentrations of the antimicrobial agent:        -   computing of a first coordinate value corresponding to the            main mode of the acquired distribution and an first area of            the acquired distribution for values greater than the first            coordinate value;        -   computing of a second coordinate value, greater than said            first coordinate value, for which a second area of the            acquired distribution between said first and second            coordinate values equals a predefined percentage of the            first area over 50%,        -   computing a ratio according to the relation:

$Q = \frac{{{QT}({ATB})} - {{Mode}({ATB})}}{{{QT}\left( {{no}\mspace{14mu} {ATB}} \right)} - {{Mode}\left( {{no}\mspace{14mu} {ATB}} \right)}}$

-   -   -   where Mode(ATB) and QT(ATB) are respectively the first and            second coordinate values with said concentration of            antimicrobial agent, and Mode(no ATB) and QT(no ATB) are            respectively the first and second coordinate values without            said concentration of antimicrobial agent

    -   e. learn, by means of a computer unit, a prediction model of the        sensibility phenotype to the antimicrobial agent based on the        generated feature vectors and the digital set of sensibility        phenotypes;

B. a prediction stage comprising the following steps:

-   -   f. prepare liquid samples comprising a population of the test        microorganism, the viability fluorescence marker and the        antimicrobial agent at the different concentrations;    -   g. for each sample of the test microorganism, acquire, by means        of a flow cytometer, a digital set of values corresponding to        the set of values acquired at step c);    -   h. generate, by means of a computer unit, a feature vector based        on the sets of values acquired for the test microorganism, said        feature vector corresponding the features vector of step d);    -   i. predict the sensibility phenotype of the test microorganism,        by means of a computer unit storing the prediction model, by        applying said model to the feature vector of the test        microorganism.

In other words, the prediction model is based on a learning set of dataderived from microorganisms having a diversity regarding theirphenotypes, and advantageously having a great diversity in terms ofGram/species/genera, concentrations of the antimicrobial agent andresponse to the antimicrobial agent. A robust prediction model, directlydetermining the phenotype sensibility amongstsusceptible/intermediate/resistant phenotypes may be derived from flow-acytometry measure of a unknown microorganism, e.g. a bacteria.

According one embodiment:

-   -   the prediction model comprises a first prediction model of the        susceptible phenotype versus the resistant and intermediate        phenotypes, and a second model of the resistant phenotype versus        the susceptible and intermediate phenotypes, said first and        second prediction models being learned independently; and    -   the intermediate phenotype is predicted when the first        prediction model does not predict the susceptible phenotype and        when the second prediction model does not predict the resistant        phenotype.

According to another embodiment, the prediction model comprises a firstprediction model of the susceptible phenotype versus the resistant andintermediate phenotypes, a second model of the resistant phenotypeversus the susceptible and intermediate phenotypes, and third predictionmodel of the intermediate phenotype versus the susceptible and resistantphenotypes, said first, second and third prediction models being learnedindependently.

According to one embodiment, the different concentration of theantimicrobial agent define a range comprising the susceptible andresistant breakpoint concentrations.

According one variant, the different concentration of the antimicrobialagent consist respectively in the susceptible and resistant breakpointconcentrations. In another variant, the different concentrations of theantimicrobial agent comprise at least three concentrations, and moreparticularly at least four concentrations.

According to one embodiment, at least one of the differentconcentrations of the antimicrobial agent is less than the susceptiblebreakpoint concentration.

According to one embodiment, the method comprises, at the learningstage, the selection of the different concentrations of theantimicrobial agent by:

-   -   selecting a first set of different concentrations comprising the        different concentrations of the antimicrobial agent and        performing steps b) to f) with all the concentrations of said        first set of different concentrations;    -   learning a prediction model of the sensibility phenotype to the        antimicrobial agent based on the generated feature vectors and        the digital set of sensibility phenotypes, wherein said learning        is performed using a L1-regularised optimization problem trading        off precision of the prediction model and complexity of the        prediction model, and wherein the different concentrations of        the antimicrobial agent are the concentrations of the first set        of concentrations that are not discarded by the L1-regularised        optimization problem.

In particular, the L1-regularised optimization problem is aL1-regularized logistic regression.

According to one embodiment, the digital set of values comprises afluorescence distribution over a predefined fluorescence range, andwherein the feature vectors comprises an histogram of the fluorescencedistribution over a subdivision of the predefined fluorescence range.

According to one embodiment, the digital set of values comprises a sidescatter distribution over a predefined side scatter value range, andwherein the feature vectors comprises an histogram of the side scatterdistribution over a subdivision of the predefined side scatter valuerange.

According to one embodiment, the digital set of values comprises aforward scatter distribution over a predefined forward scatter valuerange, and wherein the feature vectors comprises an histogram of theforward scatter distribution over a subdivision of the predefinedforward scatter value range.

In particular, the predefined percentage is over 70%, preferably equalto 75%, 90%, 95% or 99%.

According to one embodiment, the microorganisms of the set ofmicroorganisms belong to different species and/or genera.

According to one embodiment, the antimicrobial agent is an antibioticand the microorganisms are bacteria.

Another object of the invention is a method for predicting thesensibility phenotype of a test microorganism to an antimicrobial agentamongst susceptible, intermediate and resistant phenotypes, comprising:

-   -   a. prepare liquid samples comprising a population of the test        microorganism, the viability fluorescence marker targeting the        test microorganism and the antimicrobial agent at different        concentrations;    -   b. for each sample of the test microorganism, acquire, by means        of a flow cytometer, a digital set of values comprising a        fluorescence distribution and/or a forward scatter distribution        and/or side scatter distribution of the population of the test        microorganism in said sample;    -   c. generate, by means of a computer unit, a feature vector based        on the sets of values acquired for the test microorganism;    -   d. predict the sensibility phenotype of the test microorganism,        by means of a computing unit storing a prediction model, by        applying said model to the feature vector of the test        microorganism, wherein the prediction model is learned according        the learning phase as described above.

Another object of the invention is a system for predicting thesensibility phenotype of a test microorganism to an antimicrobial agentamongst susceptible, intermediate and resistant phenotypes, comprising:

-   -   a flow cytometer for acquiring a digital set of values        comprising a fluorescence distribution and/or a forward scatter        distribution and/or side scatter distribution of a population of        the test microorganism in liquid samples, said samples        comprising a viability fluorescence marker targeting the test        microorganism and different concentrations of the antimicrobial        agent and;    -   a computer unit configured for        -   storing a prediction model learned according the learning            phase as described above;        -   generating a feature vector based on the sets of values            acquired for the test microorganism; and        -   predicting the sensibility phenotype of the test            microorganism by applying the prediction model to the            feature vector of the test microorganism.

Another object of the invention is a computer readable medium storinginstruction for executing a method performed by a computer, the methodcomprising the prediction of the sensibility phenotype of a testmicroorganism to an antimicrobial agent amongst susceptible,intermediate and resistant phenotypes, said prediction comprising:

-   -   generating a feature vector based on sets of values acquired for        a test microorganism, said sets comprising a fluorescence        distribution and/or a forward scatter distribution and/or side        scatter distribution of a population of the test microorganism        in liquid samples acquired by a flow cytometer; and    -   predicting the sensibility phenotype of the test microorganism        by applying a prediction model to the feature vector of the test        microorganism,        wherein the prediction model learned according the learning        phase as described above.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood from the following non-limitingdescription, in connection with the accompanying drawings, among which:

FIG. 1 is a schematic view of a flow-cytometry system according to theinvention;

FIG. 2A is a flowchart of a learning stage according to the invention;

FIG. 2B is a flowchart of a prediction stage according to the invention;

FIG. 3 is a flowchart of a FCM-AST protocol according to the inventiondetailing the sample preparation;

FIG. 4 is a schematic representation of population distribution profilesand the methods used to generate feature vectors;

FIG. 5 is a schematic representation of the phenotype discriminationstrategies used to build phenotype prediction models;

FIG. 6 is a schematic representation of the panel of strains accordingto their MICs for Gentamicin;

FIG. 7 is a schematic representation of fluorescence distributionprofiles of Gentamicin-treated strains;

FIG. 8 is a schematic comparison of performance of 1D fluorescenceprediction models (Quantile vs. MFI);

FIG. 9 is a schematic representation of the panel of strains accordingto their MICs for Ceftazidime;

FIG. 10 is a table illustrating the number of predictions modelsgenerated;

FIG. 11 is a schematic comparison of discrimination strategies forCeftazidime;

FIG. 12 is a table of the classification of prediction models forCeftazidime; and

FIG. 13 is a schematic comparison of performance of 3D prediction models(GS) and VITEK 2.

DETAILED DESCRIPTION

Unless explicitly stated otherwise, greater means greater or equal andless means less or equal.

Referring to FIG. 1, a flow-cytometry system 10 comprises aflow-cytometer 12 and a computer unit 14 for processing data output bythe flow-cytometer 12 to learn prediction model and/or predictsensibility phenotypes of microorganisms to antimicrobial agents. Theflow-cytometer 12 comprises a fluidic system, at least one light source,an optical system comprising excitation optics and collection optics,and an electronic system. The fluidic system is designed to transportthe microorganisms of the liquid sample one at a time to aninterrogation point where a beam of the light source intersects. At thispoint light is scattered and refracted by the microorganisms and lightscatter is collected by the optic system at two angles where they areacquired by detectors, that is to say the “Forward scatter” (FSC), whichis a measurement of diffracted light in the direction of the lightsource, and the “Side scatter” (SSC), which is collected around 90° fromthe light beam. Moreover, the light source(s) is/are designed to excitefluorochromes so that fluorescence of microorganisms is also acquiredthrough the optical system by detectors. For the population ofmicroorganisms contains in the liquid sample, a FSC distribution, a SSCdistribution and a fluorescence distribution are the acquired and storedin an electronics systems which also drives the flow cytometeroperation. Flow-cytometry being well-known, it won't be furtherdetailed. For example, the flow-cytometer is a “Cyflow® Space flowcytometer” from Partec GmbH. The FSC, SSC and fluorescence distributionsare communicated to the computer unit 14, for example a personalcomputer, a tablet, a smartphone, a server, and more generally anysystem comprising one or more microprocessors and/or one or moremicrocontrollers, e.g. a digital signal processor, and/or one moreprogrammable logic device, configured to implement a digital processingof the distributions generated by the flow-cytometers 12. The computerunit 14 comprises computer memories (RAM, ROM, cache memory, massmemory) for the storing the acquired distributions, instructions forexecuting the method according to the invention, and intermediate andfinal computation, in particular the antibiotic sensibility of themicroorganisms. The computer units further comprises a screen fordisplaying said sensibility to users. While the computer unit has beendescribed as a distinct entity from the electronic system of theflow-cytometer, the computer unit and the electronic systems may beimplemented by a unique unit.

A method to predict the sensibility to an antibiotic of a bacterialstrain is now described in relation to FIG. 2, the method comprising alearning stage (FIG. 2A) and a prediction stage (FIG. 2B).

The learning stage aims a determining antibiotic sensibility phenotypepatterns in the FSC, SSC and fluorescence distributions of a set ofdifferent known strains, in particular susceptible phenotype (S)strains, intermediate phenotype (I) strains and resistant phenotype (R)strains, the sensibility phenotype to the antibiotic of each strainbeing known and determined according the EUCAT or CLSI nomenclature forexample. Advantageously, the patterns are determined to be independentas far of possible of the strains. To this end, the set of strainscomprises more than 100 hundred strains from different species and/orgenera.

The learning stage thus begins, in 20, by the selection of said set ofstrains {S₁, . . . , S_(n)}, where n is the number of strains, and bystoring their sensibility phenotypes in the computer unit 14, thephenotypes, e.g. in the form of a digital phenotype vector (P₁ . . .P_(N)), where ∀i∈[1, n], P_(i) is the sensibility phenotype of strainS_(i) to the antibiotic, i.e. P_(i)=R (resistant), I (intermediate) or S(susceptible). The antibiotic breakpoints BP_(S) (susceptiblebreakpoint) and BP_(R) (resistant breakpoint) of the antibiotic.

In a next step 22, liquid samples with different concentrations {C₁, . .. , C_(m)} of the antibiotic are prepared for each of the selectedstrains S_(i), where C₁=0 (no antibiotic) and m>2 is the number ofnon-null concentrations of antibiotic. Said concentrations are stored inthe computer unit 14. In particular, as illustrated in FIG. 3, bacterialcolonies of the strain are grown and used to make an inoculum. After 2 hgrowth at 35° C. with shaking at 180 rpm, the resulting exponentialphase bacterial culture is normalized at 0.5 McF and used to inoculatewells of a microtiterplate supplemented with antibiotics at thedifferent concentrations {C₁, . . . , C_(m)}. After 1 h of incubation at35° C., a membrane depolarization fluorescent marker, for example(Bis-(1,3-Dibutylbarbituric Acid)Trimethine Oxonol), also known as“DiBAC4(3)”, is added to the wells at a final concentration of 0.5μg/ml. An additional 15 min incubation with the marker is at 35° C. isthen carried out. The concentrations {C₁, . . . , C_(m)} are chosen suchthat the range [BP_(S), BP_(R)] is included or equal to the range [C₂,C_(m)] of non-null concentrations.

In the step 24, a FCM acquisition is performed for each sample by meansof the flow-cytometer 12 and the corresponding FSC, SSC and fluorescencedistributions stored in the computer unit 14. For each strain S_(i), andfor each concentration C₁, a FSC distribution “FSC_(i,j)”, a SSCdistribution “SSC_(i,j)” and a fluorescence distribution “FI_(i,j)” arethus stored in the computer unit 14, e.g. in the form of digitalvectors.

A processing of said distribution is performed, in 26, by the computerunit 14 in order to generate at least one feature vector X_(i,j) foreach set of distributions {FSC_(i,j), SSC_(i,j), FI_(i,j)}. Thegenerated features vectors X_(i,j) quantify the changes that occurwithin the bacterial populations following incubation with antibiotic,and are combined with digital phenotype vector (P₁ . . . P_(N)) to findphenotype patterns as described latter. In particular, feature vectorsbased on three methods, that is to say, a mean fluorescence intensity(MFI) method, a binning method and a quantile (QT) method. FIG. 4 isschematic representation of population distribution profiles and themethods used to generate feature vectors. In FIG. 4, “ATB” refers to asample with a non-null concentration of antibiotic (C_(j>1)) and “noATB” refers to a sample with no antibiotic (C₁).

In the mean fluorescence intensity method, as illustrated in FIG. 4E, afeature vector X_(i,j) is computed for a each non-null concentrationC_(j>1) according to the relation:

$X_{i,{j > 1}} = {{{MFI}\left( {i,{j > 1}} \right)} = \frac{\overset{\_}{{FI}_{i,{j > 1}}}}{\overset{\_}{{FI}_{i,1}}}}$

where FI_(ι,J>1) and FI_(ι,1) are respectively the mean values ofdistributions FI_(i,j>1) and FI_(i,1).

In figures FIGS. 4A, 4B and 4C, monoparametric histogram show three mainfluorescence distributions observed for antibiotic-treated and untreatedbacterial populations. When compared to the distribution of untreatedpopulations, antibiotic-treated bacteria exhibit either no or slightfluorescence shift (A), a fluorescence shift of the entire population(B) or a fluorescence shift of only one small portion of the population(C). The more the feature vector X_(i,j>1) differs from 1, the more thestrain is susceptible to the antibiotic. Similar distribution profilescan also be observed for SSC and FSC (not shown).

The binning method is performed on biparametric FSC-SSC distributionsand on monoparametric (“1D”) distributions of fluorescence, FSC and SSC.In particular, the range of a distribution (e.g. fluorescence) isdivided in intervals, or “bins”, and the intensities of the distributionin each bin are summed, or “binned”. For example, referring to FIG. 4D,a biparametric (“2D”) dot plot is shows the difference in scatteringprofiles between treated and untreated bacterial populations. In thisfigure, a grid of 5×5 (25 bins) is applied to the 2D plot. The number ofevents in each bin is recorded to generate a set of values defined asfeature vector. Binning is performed on biparametric FSC-SSCdistributions as shown in this example and on monoparametricdistributions of fluorescence, FSC and SSC. More precisely, thesevectors were obtained as follows:

-   -   binning of 1D SSC or FSC distribution: the dynamic range of the        signal (e.g. [1, 10000]), is cut in 5, 10, 20 or 40 bins of the        size on a logarithmic scale. The proportion of events falling in        each bin was then used to represent the entire distribution;    -   binning of 2D SSC/FSC distributions: the same procedure is        applied on the bi-dimensional space defined by the two        scattering signals, which is therefore discretized into 5×5=25,        10×10=100, 20×20=400 or 40×40=1600 bins;    -   binning of 1D fluorescence signal: the same procedure as the one        for the 1D scattering signals is applied, with the notable        exception that only the part of the distribution that is above        its mode (i.e: above the main pic at non null intensity) is        considered. The remaining part of the distribution is not        considered because the fluorescence distribution exhibits a peak        at null intensity that could greatly vary in its amplitude,        which could therefore be detrimental to the binning        representation.

In quantile method, as illustrated in FIG. 4F, a ratio of fluorescencevalues at each quantile of a set of quantiles is calculated as follows:

$X_{i,{j > 1}} = {{Q\left( {i,{j > 1},q} \right)} = \frac{{{QT}\left( {{FI}_{i,{j > 1}},q} \right)} - {{Mode}\left( {FI}_{i,{j > 1}} \right)}}{{{QT}\left( {{FI}_{i,1},q} \right)} - {{Mode}\left( {FI}_{i,1} \right)}}}$

where Mode(FI_(i,j>1)) is the fluorescence value of the main non-nullpic of the fluorescence distribution FI_(i,j>1), i.e. the fluorescenceintensity corresponding to the maximum number of events,QT(FI_(i,j>1),q) is the fluorescence value such that the area of thefluorescence distribution between said two values equal q % of the totalarea of the fluorescence distribution for fluorescence values above themode, and Mode(no ATB) and QT (no ATB) are respectively analogue valuesfor fluorescence distribution with null concentration C₁. Quantiles qare above 70%, in particular equal to 75%, 90%, 95% and 99% of the areaunder the curve from left to right.

The quantile method is designed to allow more efficient detection ofsubtle changes in the fluorescence distribution of populations uponcontact with antibiotics. Indeed, for a given strain treated with anantibiotic, three main distribution profiles that can be observed arerepresented in FIG. 4. In heterogeneous fluorescence distributions whereonly a small part of the population exhibit a strong fluorescence (FIGS.4C and 4F), the MFI method might not be appropriate since the signalwill be dominated by the non-fluorescent population. In this case thequantile method could allow to capture the signal originating from thesmall population.

Therefore, for a given strain treated with one concentration ofantibiotic, the following feature vectors are generated by the computerunit 14:

-   -   4 sets of values obtained from 1D fluorescence distributions        (binned data);    -   4 sets of values obtained from 1D SSC distributions (binned        data);    -   4 sets of values obtained from 1D FSC distributions (binned        data);    -   4 sets of values corresponding to 2D FSC-SSC distributions        (binned data)    -   1 ratio of MFI;    -   4 ratios of quantiles Q; and    -   16 sets of values obtained from the combinations of 2D FSC-SSC        distributions and 1D fluorescence distributions (3D models,        binned data).

In the next step 28 of the learning stage, the computer units selectsamongst the concentration set {C₁, . . . , C_(m)}, the concentrationswhich are the most relevant for the phenotype prediction. To this end,the unit 14 learns at least one adaptive prediction model of thesensibility phenotypes based on the generated feature vectors X_(i,j)and the vector of phenotypes (P₁ . . . P_(N)), in particular usingsupervised learning based on a L1-regularised optimization problem, asit is described later. In particular, the L1-regularized problemtrades-off between the precision of the prediction model and thecomplexity of the model. Reducing the number of concentrations shortenthe sample preparation, the flow-cytometry acquisition and dataprocessing during the phenotype prediction of an unknown strain.

Based on the selected concentrations or the whole set {C₁, . . . ,C_(m)}, the computer unit 14 learns, in a step 30, prediction model ofthe sensibility phenotypes based on the generated feature vectorsX_(i,j) and the vector of phenotypes (P₁ . . . P_(N)), in particularusing supervised learning, e.g. a support vector machine (SVM) learning.In particular, all the 1D, 2D and 3D feature vectors generated areprocessed using the three different phenotype discrimination strategiesdetailed in FIG. 5:

-   -   The breakpoint-based strategy (BPS). The BPS strategy is based        on two matrices that predict S and R phenotypes, respectively.        Intermediate phenotypes are predicted by elimination when they        don't fall in any of the two matrices;    -   The global strategy (GS). The GS strategy is also based on two        matrices for S and R and Intermediate phenotypes are also        predicted by elimination. As opposed to the BPS strategy, GS can        build prediction models by processing data from more than one        antibiotic concentration in each matrix;    -   The global multiclass strategy (GMS). The GMC strategy is based        on 3 matrices that predict S, I and R phenotypes, respectively.        Similar to GS, the GMC strategy can also process data from more        than one antibiotic concentration in each matrix.

As described in FIG. 5, in which 4 concentrations C1, C2, C3 and C4 areexemplified: (A) in the breakpoint-based strategy (BPS), feature vectorsgenerated following FCM analysis of strains are processed in twomatrices. The first matrix processes the feature vectors generated afterincubation of strains with a concentration of antibiotic correspondingto the susceptible reference breakpoint (feature vector for BP_(S)). Inthis matrix, a cutoff is calculated to discriminate S phenotype from Ior R phenotypes. The second matrix processes the feature vectorsgenerated following incubation of strains with a concentration ofantibiotic corresponding to the resistance reference breakpoint (featurevector for BP_(R)). In this matrix, another cutoff is calculated todiscriminate R phenotype from S or I phenotypes. Strains that are notpredicted as S in the first matrix and R in the second matrix areclassified as I. (B) The global strategy (GS) is also based on twomatrices that predict S and R phenotypes, respectively. Both matricesprocess feature vectors generated following incubation of strains withall concentrations of antibiotics investigated (ex: C1 to C4). (C) Theglobal multiclass strategy (GMS) is based on three matrices. Eachphenotype is differentiated in a separate matrix from the two otherphenotypes. This strategy also process feature vectors generated for allantibiotic concentrations investigated.

MIC concentrations determined by the reference microdilution method isnot always correlated with the concentrations that induce the mostsignificant early changes by FCM using a specific protocol. In thisregard, other FCM-based studies have rather investigated the effect ofantibiotics using subinhibitory concentrations [6] or concentrationsexceeding MIC values [18, 19]. Therefore, by using only the BPS strategywith the susceptible and the resistant breakpoint concentrations,important information that originate from neighboring antibioticconcentrations may be missed. In the global strategies according to theinvention (GS and GMS), the prediction models are built on additionalconcentrations in order to integrate additional antibiotic-inducedchanges, if any, that may help to better discriminate betweenphenotypes.

To build the predictive models, two different strategies were set-updepending on the nature of the data representation:

-   -   for the BPS strategy operating on the fluorescence signal        represented by a MFI or the quantile-based indicator Q, each        microorganism was represented by a single value, this values        being not the same to build the models in charge of predicting S        and R phenotypes because they were computed from different        antibiotic concentrations. The classification rule has a simple        form in this case and simply amounted to setting a threshold on        the MFI or Q. To optimize this threshold, a ROC curve analysis        is used, as detailed below;    -   in all other cases, each microorganism was represented by        several values (e.g., several MFI or Q values for the GS and GMC        strategies, or a vector containing one or several binned        distribution(s) for the BPS, GS and GMC strategies). In these        cases, the Support Vector Machine (SVM) algorithm is implemented        by the computer unit to learn a classification rule converting        such multi-dimensional feature vectors into a classification        rule, as detailed below.

The procedure to build the BPS, GS and GMC models is the same in bothcases:

-   -   for the BPS and GS strategy, two models in charge of identifying        S and R strains are independently built. Both models are binary        classification models, the first one seeking to separate S        strains from {I and R} strains and the second one seeking to        separate R strains from {S and I}. The difference between the        BPS and GS strategy solely resided in the amount of information        provided to the learning algorithm. With the BPS strategy, the        sole antibiotic concentration considered to learn each of the {R        vs S-I} and {S vs R-I} model was the one that corresponded to        the associated breakpoint. This therefore meant that the data        provided to the algorithm to learn each model was not the same.        Conversely, in the GS strategy, every antibiotic concentration        available is considered to learn each model. This therefore mean        that the data provided to the algorithm to learn each model is        the same, and is typically m-1 times longer than the one        provided to the BPS strategy, advantageously m-1=4, 4        concentrations being considered to characterize strains to a        given antibiotic);    -   For the GMC strategy, a “one versus all” SVM multiclass model is        built to directly identify R, S and I strains. For that purpose,        three models are constructed, each in charge of separating        strains of one category from strains of the two other ones. This        contrasted with the above approaches in which I strains are        identified by elimination (strains that were neither classified        as R nor S).

To build more efficient classification rules, the parameters involved inthe learning algorithms are optimized, e.g. the regularization parameter(sometimes called “C”) of the SVM for multi-dimensional signalrepresentations, the threshold to consider on the MFI or Q values(mono-dimensional representation) in a receiver operating characteristic(ROC) curve. In particular, those parameters are optimized bycross-validation, the general principle thereof being sketched asfollows:

-   -   Split the dataset in a pre-determined number K of even subsets,        or “folds”, with K typically set to 5 or 10;    -   Carry out an iterative procedure in which:        -   Leave aside one of the K subsets of the data        -   Learn the classification model from the (K−1) remaining            subsets, for different values of the model parameter to            optimize        -   Evaluate the predictions on the held out subset, for the            different candidate models, corresponding to the different            values of the model parameter.    -   Evaluate the classification performance measured on the entire        dataset for the different candidate values of the model        parameter;    -   Choose the value maximizing the classification performance.

The final model are then built from the entire dataset using the optimalparameter values, and are used to make predictions on new samples.

To learn the regularization parameter of the SVM involved in themulti-dimensional representations of the BPS, GS and GMC strategies, weproceeded this way using the grid of candidate value defined as {10⁻⁴,10^(−3.5),10⁻³, . . . , 10³, 10^(3.5),10⁴}. In the case of theuni-dimensional representation of the MFI- and R-based BPS strategy, thefollowing process is implemented:

-   -   To define candidate thresholds, a ROC curve is first built for        each of the two models in charge of identifying R and S strains        from the remaining ones;    -   then 6 candidate thresholds corresponding to true positive rates        (or sensitivities) of {0.7, 0.75, 0.8, 0.85, 0.9, 0.95} are        extracted, the positive class corresponding to the class        targeted by each model (i.e., R for the model in charge of        identifying R strains and S for the other one).

In a next step 32, the performance of each of the prediction models isthereafter computed by the unit 14. In particular, the prediction modelsgenerated are evaluated through cross validation and the number ofphenotype prediction errors recorded are classified as follows:

-   -   minor errors (mE)=I predicted S or R, S predicted I or R        predicted I;    -   major errors (ME)=S predicted R;    -   very major errors (VME)=R predicted S

To evaluate the classification performance of the various modelsconsidered, a nested cross-validation scheme is implemented in which thedataset is split into K subsets and an iterative procedure is carriedout in which:

-   -   the parameters involved in the model using (K−1) subsets of the        dataset are optimized. For this purpose, we rely on the        cross-validation procedure described previously;    -   the predictions on the remaining subset is evaluated.

This procedure is standard to evaluate performance on classificationmodels, and has the interest on integrating the step of parameteroptimization in the estimation of the model performance. In practice,this procedure is repeated several times, e.g. 10 times, in order to berobust to the random splitting of the dataset into subsets, and in orderto consider the average performance obtained across repetitions. A scorebased on the number of prediction errors is computed by the computerunit 14 for each prediction model using the following formula:

Score=Number(mE)×p1+Number(ME)×p2+Number(VME)×p3

where p1>p2>p3 are positive number, for example respectively equal to 1,2 and 4.

Prediction errors are thus rated according to their relative clinicalimportance, e.g. as defined in US Federal Drug Administration acceptancecriteria. The model exhibiting the lowest score is defined as the bestprediction model. The best prediction model is then stored, in a step34, in a computer memory.

Turning back to concentration selection step 28, the global strategies(GS and GMS) aim to integrate additional information to improvediscrimination potential of prediction models. However, depending on thebug/drug combination investigated, additional concentrations can eitherimprove, reduce or have no effect on the discrimination potential ofprediction models. For instance, high concentrations of antibiotics caninduce rapid lysis of susceptible cells leading to a loss of informationin FCM analysis. Concentrations higher than resistant breakpointconcentrations can also damage cells exhibiting low level of resistanceand change their FCM resistance profiles into susceptible ones. In thecase where our global strategies provide better prediction models thanthe BPS, the question remains as to what are the most relevantconcentrations to be used. For instance, if 4 concentrations areinvestigated (C1, C2, C3 and C4), 15 theoretical combinations ofrelevant concentrations are possible for a given antibiotic. In order toassess which one of this combination is the most relevant, aL1-regularized Logistic-Regression, or Lasso Logistic-Regression, isimplemented to build prediction models that only consider the mostrelevant concentrations. The main advantage of this method is that itcan allow:

-   -   to reduce the amount of reagent (ex: if only 1 out 4        concentrations tested is relevant for optimal discrimination);    -   to reduce the time of FCM acquisition (ex: Less tubes or wells        will have to be analyzed if just one concentration is relevant);    -   to select the most appropriate concentrations (ex: if the most        relevant concentrations are not necessarily breakpoint        concentrations)

Hence, this tool can help to optimize the development of a FCM protocolfor a given bug/drug combination and a given viability marker. As it iswell-known, the L1-regularized Logistic Regression is very similar tothe SVM. The main difference resides in a different regularizationfunction. The standard SVM includes a regularization term defined interms of the Euclidean or L2 norm of its weight vector (e.g.:∥w∥²=(Σ(w_(i))²)^(1/2), where w is the vector of the decision variablein a SVM learning). Considering the L1 norm instead of the Euclideannorm amounts to considering the quantity ∥w∥₁=Σ|w_(i)| as regularizationterm. Both definitions have the effect of limiting the magnitude of theweights, which is crucial to learn in high dimensions, but the L1penalty has a well-known “sparsity” effect leading to weights that canbe not only small, but exactly equal to zero, which will never happenwith the L2 penalty. As a result, using this penalty in a SVM (or aLogistic Regression) allows to automatically select variables that arerelevant for the model. In this context, this allows to automaticallydiscard concentrations that may not be informative. Applying the L1penalty to multivariate MFI and R representations is straightforward. Toapply the L1 penalty to binning data gathering several antibioticconcentrations, a more advanced analytical tool called the “group lasso”penalty is performed. Indeed, a concentration may be discarded if allthe features corresponding to its binning representation are jointly setto zero. In order to achieve this, a grouping structure, regrouping allthe features coming from a given concentration in the same group, isused. The group-lasso penalty then achieves sparsity at the group level,hence at the concentration level. This algorithm is for exampledescribed in [22,23].

It is now described in reference to FIG. 2B, a prediction stageaccording to the invention. This prediction stage aims at determiningthe sensibility phenotype of a particular strain, e.g. an unknown strainor a strain whose species is known but whose sensibility phenotype isunknown. The prediction stage is embodied using a system analogue to thesystem described in the FIG. 1, e.g. installed in a clinical laboratory,that is to say a system comprising a flow cytometer and a computer unitconnected to the flow cytometer storing in a memory the prediction modelselected during the learning stage. The flow cytometer is advantageouslyof the same model and is operated with the same control parameters thanthe flow cytometer used in the learning state. The computer unit may befor example computer located at the same place than the flow cytometeror a server located at a remote location which performs a cloudcomputing based on the data communicated by the flow cytometer over acommunication network, e.g. the Internet.

The prediction stage begins, in a step 36, by the preparation of liquidsamples of the strains as described above with the concentrationscorresponding to the prediction model stored in the computer unit, e.g.the whole set of concentrations or the selected concentrations. In thefollowing step 38, the FFC, SSC and fluorescence distributions areacquired and stored in the computing unit. The latter then generates, in40, feature vectors having the same format than the ones used to learnthe prediction model, and the, in 42, the computer unit applies theprediction model to the generated feature vectors, thereby outputting asensibility phenotype S, I or R for the tested strain. The result of theprediction is then store in a computer memory and/or display on a screenin a step 44.

While it has been described a systematic approach to learn the bestmodel amongst a wide variety of predictions models, the learning stagemay perform the learning of a single prediction model, for example inthe case where one knows beforehand which type of model is the best fora particular antibiotic. For example, quantile ratio have very goodperformance for antibiotic inducing heterogonous fluorescence profilesas illustrated in FIG. 4C. In such case, only the distribution necessaryfor the feature vectors generation may be acquired, only the featurevectors used for the prediction model learning and implementation aregenerated (e.g. at least one of the quantile ratios or all the quantileratios), and only the selected prediction model is learned andimplemented.

Moreover, the quantile ratio Q may be used alone to quantify the effectof the antibiotic on a bacterial. In particular, a method forquantifying this effect comprises the preparation of a first sample witha concentration of the antibiotic, of a second sample with nonantiobiotic, and the computation by the computing unit of the ratio Qfor this two sample has described above. The ratio Q may be for examplestored and/or displayed on a screen to the attention of a user.

Moreover, the quantile method may also be implemented on FSC or SSCdistributions. In such case, optionally and advantageously, nofluorescent marker is used.

The invention also applies to the following:

-   -   FCM-AST from biological samples or microbial extracts;    -   Other viability markers or multi-labelling can be used;    -   Can be applied to all species and antibiotics/antifungals;    -   The rating of errors can be adjusted to enhance the prediction        of a particular phenotype;    -   The quantile method can also be applied to FSC and SSC        monoparametric distributions;    -   The quantile method can also be used to detect heterogeneous        populations (ex: hVISA);    -   More than 4 configurations can be investigated for Binning and        Quantile methods;    -   3D models can also be built by combining 1D feature vectors        obtained from the binning method;    -   3D models can also be built by combining 1D feature vectors        obtained from quantile or MFI methods;    -   2D models including scattering and fluorescence can also be        investigated;    -   Autofluorescence of cells can also be added as an additional        parameter for analysis.

While it has been described the sensibility phenotype prediction of abacteria to an antibiotic, the present invention also applies to yeastand fungus.

Performance Evaluation of Phenotype Prediction Algorithms A. Experiment1: Evaluation of Quantile-Based Prediction Models for HeterogeneousFluorescence Distributions

A.i. Fluorescence Distribution Profiles of Gentamicin-Treated Strains

The experiment was performed as described in the following lines:

-   -   A panel of 107 Enterobacteriaceae strains (FIG. 6: Distribution        of the panel of strains according to their MICs for Gentamicin)        were treated with 0, 2, 4 and 8 mg/L of Gentamicin following the        protocol described in FIG. 3 and analyzed by FCM. Reference        phenotypes of all strains were determined by broth microdilution        method according to CLSI breakpoints;    -   Fluorescence distribution were observed for all strains and        classified based on their profiles;    -   Prediction models were generated from FCM data and the        performance was evaluated as described above.

FCM fluorescence distribution obtained from Gentamicin-treated samplesshowed 3 main profiles when compared to untreated samples (FIG. 7:Spectra from 3 susceptible strains which are representative of the 3main profiles A, B and C are shown. Within our panel of 107 strains, thenumber of strains exhibiting one of the three profiles are shown at eachGentamicin concentration investigated and for each phenotype (table).Cells filled in grey represent the highest number of strains exhibitinga specific profile for a given antibiotic concentration):

-   -   Profile A: no or slight shift of fluorescence distribution;    -   Profile B: heterogeneous distribution with one non fluorescent        population and a small fluorescent population;    -   Profile C: Significant shift of the fluorescence distribution.

Within the panel of 107 strains, the distribution of profiles wereapproximately evaluated as follows (FIG. 7, table):

-   -   For the susceptible phenotype, equal number of strains exhibited        either no shift (profile A) or heterogeneous fluorescence        distributions (profile B) when treated with the lowest        Gentamicin concentration (2 mg/L). When treated with 4 and 8        mg/L of Gentamicin, the majority of strains exhibited an        heterogeneous fluorescence distribution (profile B);    -   Almost all (36 out of 37) resistant strains did not show any        shift in fluorescence (profile A) at all concentrations tested;    -   For the intermediate phenotype, more strains showed no shift of        fluorescence (profile A) when treated with the lowest        concentration (2 mg/L). When treated with 4 and 8 mg/L of        Gentamicin equal number of strains exhibited either no shift        (profile A) or heterogeneous fluorescence distribution (profile        B).

These observations suggest a predominance of heterogeneous fluorescencedistributions for susceptible strains when treated with Gentamicin. Thedistribution profiles of resistant strains are highly consistent at allconcentrations. Profile of intermediate strains are more variabledepending on the concentrations used.

A.ii. Performance of Quantile-Based Vs. MFI-Based Prediction Models

As hypothesized above, the use of the MFI method might not beappropriate when heterogeneous fluorescence distributions are found.Relative to our observations within our panel of strains (FIG. 7), wehave compared the performance of BPS prediction models that were builtusing feature vectors generated from quantile and MFI methods.

Following cross validation, our results show that the performance ofprediction models are significantly higher for the quantile method whencompared to MFI. All 4 prediction models generated with quantile-basedfeature vectors showed lower score values than the one built with MFIdata (FIG. 8: The scores relative to the number of errors are shown for4 prediction models generated with quantile feature vectors (q=0.75,q=0.9, q=0.95 q=0.99) and for 1 prediction model built with MFI featurevectors. For each histogram, the mean and the maximum score values areshown. The scales corresponding to the score values are shown on theleft. The table at the bottom, shows the mean score values and theaverage number of prediction errors (mE, ME and VME). Total number ofstrains (Total), total number of susceptible strains (Total S) and totalnumber of resistant strains (Total R) are also shown).

The performance of the best quantile-based model (q=0.95) wassignificantly better than the MFI-based model with a lower score and ahigher percentage of category agreement with less of the 3 type ofprediction errors (FIG. 8, table). The score values of the 4 predictionmodels built with quantile data, can also be represented as aparabolic-like curve that could be correlated with the small fluorescentpopulation shown in FIG. 7 (profile B). This confirms the high potentialof this small population in discriminating between phenotypes. Ourresults also suggest that a more in-depth investigation between q=0.9and q=0.95 or between q=0.95 and q=0.99 could help to build a predictionmodel with better performance.

B. Experiment 2: In-Depth FCM Analysis and Selection of PredictionModels

B.i. Performance Evaluation of Discrimination Strategies

In this experiment, we have made an evaluation of wide range ofprediction models for Ceftazidime:

-   -   128 Enterobacteriaceae strains (FIG. 9: Distribution of the        panel of strains according to their MICs for Ceftazidime) were        treated or not with four different concentrations of Ceftazidime        (1, 2, 4 and 8 mg/L) using the FCM protocol described in FIG. 3;    -   FCM data were used to generate feature vectors as described        above;    -   For each strategy (BPS, GS and GMS), 7 type of prediction models        were built based on the feature vectors generated (FIG. 10:        Number of predictions models generated. “FL1” means        fluorescence);    -   The performance of all models were evaluated following cross        validation as described above.

As shown in FIG. 10, 37 prediction models were generated for eachdiscrimination strategy which makes a total number of 111 predictionmodels. The prediction model showing the lowest scores in each of the 7type of prediction models was considered thereby leading to a condensedselection of 21 models. The GS and GMS strategies showed betterdiscriminating performance (lower error scores) than the BPS strategyfor all 7 type of prediction models generated (FIG. 11: Comparison ofdiscrimination strategies for Ceftazidime. Each graph represents thelowest scores obtained for each of the 7 type of prediction modelsgenerated. The 3 strategies (BPS, GS and GMS) are compared.):

-   -   The GS strategy showed the lowest scores for 4 type of        predictions models (1D FL1 QT, 1D SSC Binning, 2D FSC-SSC        Binning and 3D FSC—SSC-FL1 Binning);    -   The GMS strategy showed the lowest scores for 3 type of        predictions models (1D FL1 MFI, 1D FL1 Binning and 1D FCS        Binning)

B.ii. Selection of the Best Prediction Model for Ceftazidime

The condensed selection of 21 prediction models were classifiedaccording to their error scores (FIG. 12: Classification of predictionmodels for Ceftazidime. BP=BPS. G=GS. GMC=GMS). According to ourclassification, the best prediction models for Ceftazidime is a 3DFSC—SSC-FL1 model built with the GS strategy. One observes thefollowing:

-   -   It is interesting to note that the 1D SSC Binning (GS)        prediction algorithm also showed relatively good performance        (FIG. 12). This suggests that the FL1 and FSC parameters only        slight contribute to the discrimination potential of the 3D        model algorithm selected. Therefore, our analysis method and        classification of prediction models might help to significantly        simplify the FCM-AST protocol (no viability marker needed for        the 1D SSC Binning (GS) model) as well as FCM acquisition        parameters (only SSC). On the other hand, we can assume that the        use of a different viability marker can significantly improve        the discrimination potential of the 3D model for even better        prediction performance;    -   The prediction models built on quantile data are the less        performing ones. This suggests that the majority of strains        treated with Ceftazidime exhibit homogeneous distributions of        fluorescence.

C. Experiment 3: Selection of Relevant Antibiotic Concentrations

As shown in FIG. 12, the best prediction model for Ceftazidime is a 3Dmodel that was built using the GS strategy. This model processes fourconcentrations of Ceftazidime (1, 2, 4 and 8 mg/L). In an effort toinvestigate the relevance of these concentrations in the discriminatingpotential of the 3D model, we have used the Lasso analytical tool tobuild a 3D model based on GS strategy as described above.

The 3D prediction model obtained using the Lasso tool showed relativelygood performance with an error score slightly higher the score of the 3Dmodel obtained with SVM analysis (FIG. 13: Performance comparison of 3Dprediction models (GS) and VITEK 2. The confusion matrices show thecorrelation and discrepancies between the reference phenotype and thephenotypes predicted by the 3D models and VITEK® 2 from bioMérieux. Thetable at the bottom, shows the mean score values and the average numberof prediction errors (mE, ME and VME). Total number of strains (Total),total number of susceptible strains (Total S) and total number ofresistant strains (Total R) are also shown. Non-relevant concentrationsof Ceftazidime in the Lasso analysis are indicated.).

Our panel of strains was also investigated using our commercial VITEK 2system. For the sake of comparison, we have not used the VITEK® 2Advanced Expert System that corrects potential prediction errors througha more global interpretation of results from other antibiotics. Instead,the predicted phenotypes shown for VITEK 2 were interpreted only fromMIC values obtained for Ceftazidime. Overall, the performance of our 3Dmodels were comparable to that of the VITEK® 2 system (FIG. 13). Thisconfirms the high phenotype discrimination power of our predictionmodels.

One observes that:

-   -   The 3D model built with Lasso only uses two concentrations (2        and 8 mg/L) which suggests that we could reduce the number of        concentrations to be used for the development a FCM-AST        application for Ceftazidime;    -   In our BPS strategy, the concentrations used are 4 mg/L in the        susceptible phenotype matrix and 8 mg/L in the resistance        phenotype matrix. In our Lasso analysis the concentration of 4        mg/L is non-relevant and 2 mg/L is preferentially used. This        confirms that the most discriminating concentrations in FCM        investigations are not necessarily breakpoint concentrations.        This might explain why the 3D model built using the BP strategy        is the least performing of the 3D models (FIG. 13).

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1. A method for quantifying the sensibility of a test microorganism to aconcentration of an antimicrobial agent comprising: preparing at a twoliquid samples comprising a population of the test microorganism and aviability fluorescence marker targeting the tested microorganism, one ofsaid liquid sample comprising the antimicrobial agent at saidconcentration and the another of said liquid samples do not comprisingthe antimicrobial agent; for each of said samples of the testmicroorganism, acquiring, by means of a flow cytometer, a digital set ofvalues comprising a fluorescence distribution or a forward scatterdistribution or side scatter distribution of the population ofmicroorganisms in said sample; for each of said samples, computing of: afirst coordinate value corresponding to the main mode of the acquireddistribution and an first area of the acquired distribution for valuesgreater than the first coordinate value; a second coordinate value,greater than said first coordinate value, for which a second area of theacquired distribution between said first and second coordinate valuesequals a predefined percentage of the first area over 50%, computing aratio according to the relation:$Q = \frac{{{QT}({ATB})} - {{Mode}({ATB})}}{{{QT}\left( {{no}\mspace{14mu} {ATB}} \right)} - {{Mode}\left( {{no}\mspace{14mu} {ATB}} \right)}}$where Mode(ATB) and QT(ATB) are respectively the first and secondcoordinate values with said concentration of antimicrobial agent, andMode(no ATB) and QT (no ATB) are respectively the first and secondcoordinate values without said concentration of antimicrobial agent. 2.A method for predicting the sensibility phenotype of a testmicroorganism to an antimicrobial agent amongst susceptible,intermediate and resistant phenotypes, comprising: A. a learning stagecomprising the following steps: a. choose a set of microorganismscomprising susceptible, intermediate an resistant phenotypemicroorganisms, said phenotypes being determined based on a susceptibleand a resistant breakpoint concentrations of the antimicrobial agent,and generate a digital set of sensibility phenotypes of said set ofmicroorganisms; b. for each microorganism of the set of microorganisms,prepare liquid samples comprising a population of said microorganism, aviability fluorescence marker targeting said microorganism, and theantimicrobial agent, said liquid samples comprising at least twodifferent concentrations of the antimicrobial agent; c. for each sample,acquire, by means of a flow cytometer, a digital set of valuescomprising a fluorescence distribution and/or a forward scatterdistribution and/or side scatter distribution of the population ofmicroorganisms in said sample; d. for each microorganism of the set ofmicroorganisms, generate, by means of a computer unit, a feature vectorbased on the sets of values acquired for said microorganism, whereingeneration of the feature vector comprises, for each of the differentconcentrations of the antimicrobial agent: computing of a firstcoordinate value corresponding to the main mode of the acquireddistribution and an first area of the acquired distribution for valuesgreater than the first coordinate value; computing of a secondcoordinate value, greater than said first coordinate value, for which asecond area of the acquired distribution between said first and secondcoordinate values equals a predefined percentage of the first area over50%, computing a ratio according to the relation:$Q = \frac{{{QT}({ATB})} - {{Mode}({ATB})}}{{{QT}\left( {{no}\mspace{14mu} {ATB}} \right)} - {{Mode}\left( {{no}\mspace{14mu} {ATB}} \right)}}$where Mode(ATB) and QT(ATB) are respectively the first and secondcoordinate values with said concentration of antimicrobial agent, andMode(no ATB) and QT(no ATB) are respectively the first and secondcoordinate values without said concentration of antimicrobial agent e.learn, by means of a computer unit, a prediction model of thesensibility phenotype to the antimicrobial agent based on the generatedfeature vectors and the digital set of sensibility phenotypes; B. aprediction stage comprising the following steps: f. prepare liquidsamples comprising a population of the test microorganism, the viabilityfluorescence marker and the antimicrobial agent at the differentconcentrations; g. for each sample of the test microorganism, acquire,by means of a flow cytometer, a digital set of values corresponding tothe set of values acquired at step c); h. generate, by means of acomputer unit, a feature vector based on the sets of values acquired forthe test microorganism, said feature vector corresponding the featuresvector of step d); i. predict the sensibility phenotype of the testmicroorganism, by means of a computer unit storing the prediction model,by applying said model to the feature vector of the test microorganism.3. Method according to claim 2: wherein the prediction model comprises afirst prediction model of the susceptible phenotype versus the resistantand intermediate phenotypes, and a second model of the resistantphenotype versus the susceptible and intermediate phenotypes, said firstand second prediction models being learned independently; and whereinthe intermediate phenotype is predicted when the first prediction modeldoes not predict the susceptible phenotype and when the secondprediction model does not predict the resistant phenotype.
 4. Methodaccording to claim 3, wherein the prediction model comprises a firstprediction model of the susceptible phenotype versus the resistant andintermediate phenotypes, a second model of the resistant phenotypeversus the susceptible and intermediate phenotypes, and third predictionmodel of the intermediate phenotype versus the susceptible and resistantphenotypes, said first, second and third prediction models being learnedindependently.
 5. Method according to claim 2, wherein the differentconcentration of the antimicrobial agent define a range comprising thesusceptible and resistant breakpoint concentrations.
 6. Method accordingto claim 2, wherein the different concentration of the antimicrobialagent consist respectively in the susceptible and resistant breakpointconcentrations.
 7. Method according to claim 2, wherein the differentconcentrations of the antimicrobial agent comprise at least threeconcentrations.
 8. Method according to claim 2, wherein at least one ofthe different concentrations of the antimicrobial agent is less than thesusceptible breakpoint concentration.
 9. Method according to claim 2,comprising, at the learning stage, the selection of the differentconcentrations of the antimicrobial agent by: selecting a first set ofdifferent concentrations comprising the different concentrations of theantimicrobial agent and performing steps b) to f) with all theconcentrations of said first set of different concentrations; learning aprediction model of the sensibility phenotype to the antimicrobial agentbased on the generated feature vectors and the digital set ofsensibility phenotypes, wherein said learning is performed using aL1-regularised optimization problem trading off precision of theprediction model and complexity of the prediction model, and wherein thedifferent concentrations of the antimicrobial agent are theconcentrations of the first set of concentrations that are not discardedby the L1-regularised optimization problem.
 10. Method according toclaim 9, wherein the L1-regularised optimization problem is aL1-regularized logistic regression.
 11. Method according to claim 2,wherein the microorganisms of the set of microorganisms belong todifferent species and/or genera.
 12. Method for predicting thesensibility phenotype of a test microorganism to an antimicrobial agentamongst susceptible, intermediate and resistant phenotypes, comprising:a. prepare liquid samples comprising a population of the testmicroorganism, the viability fluorescence marker targeting the testmicroorganism and the antimicrobial agent at different concentrations;b. for each sample of the test microorganism, acquire, by means of aflow cytometer, a digital set of values comprising a fluorescencedistribution and/or a forward scatter distribution and/or side scatterdistribution of the population of the test microorganism in said sample;c. generate, by means of a computer unit, a feature vector based on thesets of values acquired for the test microorganism; d. predict thesensibility phenotype of the test microorganism, by means of a computingunit storing a prediction model, by applying said model to the featurevector of the test microorganism, wherein the prediction model islearned according the learning phase of claim
 2. 13. Method according toclaim 1, wherein the acquired distribution is a fluorescencedistribution, and wherein the coordinate values are fluorescence values.14. Method according to claim 1, wherein the predefined percentage isover 70%.
 15. Method according to claim 1, wherein the antimicrobialagent is an antibiotic and the microorganisms are bacteria.
 16. A systemfor predicting the sensibility phenotype of a test microorganism to anantimicrobial agent amongst susceptible, intermediate and resistantphenotypes, comprising: a flow cytometer for acquiring a digital set ofvalues comprising a fluorescence distribution and/or a forward scatterdistribution and/or side scatter distribution of a population of thetest microorganism in liquid samples, said samples comprising aviability fluorescence marker targeting the test microorganism anddifferent concentrations of the antimicrobial agent and; a computer unitconfigured for storing a prediction model learned according the learningphase claim 2; generating a feature vector based on the sets of valuesacquired for the test microorganism; and predicting the sensibilityphenotype of the test microorganism by applying the prediction model tothe feature vector of the test microorganism.
 17. A computer readablemedium storing instruction for executing a method performed by acomputer, the method comprising the prediction of the sensibilityphenotype of a test microorganism to an antimicrobial agent amongstsusceptible, intermediate and resistant phenotypes, said predictioncomprising: generating a feature vector based on sets of values acquiredfor a test microorganism, said sets comprising a fluorescencedistribution and/or a forward scatter distribution and/or side scatterdistribution of a population of the test microorganism in liquid samplesacquired by a flow cytometer; and predicting the sensibility phenotypeof the test microorganism by applying a prediction model to the featurevector of the test microorganism, wherein the prediction model learnedaccording the learning phase of claim 2.